Randomized methods for rank-deficient linear systems
Josef Sifuentes, Zydrunas Gimbutas, Leslie Greengard
We present a simple, accurate method for solving consistent, rank-deficient linear systems, with or without additional rank-completing constraints. Such problems arise in a variety of applications, such as the computation of the eigenvectors of a matrix corresponding to a known eigenvalue. The method is based on elementary linear algebra combined with the observation that if the matrix is rank-k deficient, then a random rank k perturbation yields a nonsingular matrix with probability 1.
, Gimbutas, Z.
and Greengard, L.
Randomized methods for rank-deficient linear systems, Electronic Transactions on Numerical Analysis, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=915064
(Accessed December 7, 2021)